The difference between simple and compound interest (compounded annually) on a s

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Question

The difference between simple and compound interest (compounded annually) on a sum of money for 2 years at 10% per annum is 65. The sum is

Options:

A . 6500

B . 65650

C . 6565

D . 65065

Answer: Option A
Answer: (a)Let the sum be x. Then,C.I. = $x(1 + 10/100)^2 - x = {21x}/100$S.I. = ${x × 10 × 2}/100 = x/5$C.I. - S.I. = ${21x}/100 - x/5 = x/100$Given that, $x/100$ = 65x = 6500Hence, the sum is Rs.6500.Using Rule 6,Here, C.I. - S.I. = Rs.65, R = 10%, T = 2 years, P = ?C.I. - S.I. = P$(R/100)^2$65 = P$(10/100)^2$ ⇒ P = Rs.6500

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